"I go that way."
Translation:저는 그쪽으로 갑니다.
In terms of movement(!) it is used when you want to say you're taking a specific direction.
Unfortunately this -(으)로 has a lot of other uses, but you can often use -에 as well as -로 for going somewhere. The difference is you can use -로 for things that aren't places, like 그쪽으로, or 언덕 위로 (to the top of the hill).